There is hole of area 'A' at the bottom of a cylindrical vessel. Water is filled to a height ' h ' and water flows out in ' t ' second. If water is filled to a height ' 4 ~h ', it will flow out in time (in second)

Step-by-step solution

From equation of continuity, A v₁=a₂ A (- dh dt )= a 2 gh _ h ₁ ^ h ₂ - dh h = ₀^ t a A 2 ~g dt -[2 h ]_ h ₁ ^ h ₂ = a A 2 ~g t 2 ( h ₂ - h ₁ )= a A 2 gt t= 2 A a H 2 g = A a 2 H g For height h , the time is t₁= A A₀ 2 h g For height 4 ~h , the time is t₂= A A₀ 8 h g t₂ t₁ =2 t ₂=2 t ₁ t ₂=2 t ( t ₁= t )